8 citations · 25 across the 9 of their papers we have counts for
12 papers
Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases
Peter G. Casazza, John I. Haas, Joshua Stueck +1
We continue the study of optimal chordal packings, with emphasis on packing subspaces of dimension greater than one. Following a principle outlined in a previous work, where the au…
Phase Retrieval in $\ell_2(\RR)$
Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng +2
We will review the major results in finite dimensional real phase retrieval for vectors and projections. We then (1)prove that many of these theorems hold in infinite dimensions, (…
A short history of frames and quantum designs
Bernhard Bodmann, John Haas
In this survey, we relate frame theory and quantum information theory, focusing on quantum 2-designs. These are arrangements of weighted subspaces which are in a specific sense opt…
Low frame coherence via zero-mean tensor embeddings
Bernhard G. Bodmann, John I. Haas
This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large t…
Phase retrieval by hyperplanes
Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng +4
We show that a scalable frame does phase retrieval if and only if the hyperplanes of its orthogonal complements do phase retrieval. We then show this result fails in general by giv…
Constructions of biangular tight frames and their relationships with equiangular tight frames
John I. Haas, Jameson Cahill, Janet Tremain +1
We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner pr…
On the structures of Grassmannian frames
John I. Haas, Peter G. Casazza
A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achiev…
Toward the Classification of Biangular Harmonic Frames
Peter G. Casazza, Amineh Farzannia, John I. Haas +1
Equiangular tight frames (ETFs) and biangular tight frames (BTFs) - sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two…
Maximal Orthoplectic Fusion Frames from Mutually Unbiased Bases and Block Designs
Bernhard G. Bodmann, John I. Haas
The construction of optimal line packings in real or complex Euclidean spaces has shown to be a tantalizingly difficult task, because it includes the problem of finding maximal set…
On the rigidity of geometric and spectral properties of Grassmannian frames
Peter G. Casazza, John I. Haas
We study the rigidity properties of Grassmannian frames: basis-like sets of unit vectors that correspond to optimal Grassmannian line packings. It is known that Grassmannian frames…
Achieving the orthoplex bound and constructing weighted complex projective 2-designs with Singer sets
Bernhard G. Bodmann, John Haas
Equiangular tight frames are examples of Grassmannian line packings for a Hilbert space. More specifically, according to a bound by Welch, they are minimizers for the maximal magni…
Frame potentials and the geometry of frames
Bernhard G. Bodmann, John Haas
This paper concerns the geometric structure of optimizers for frame potentials. We consider finite, real or complex frames and rotation or unitarily invariant potentials, and mostl…